yes.
If you design and size your duct system appropriately. My 6" fan moves 500 CFM through my system. I measured it.
You need about 80 - 100 CFM per light.
My 6" fan was cooling 3 600W hoods easily.
It is about to be hooked up to 3 600W and 2 1000W
For that fan to actually move 500CFM it needs to be at least 14" duct at the fan. I use 8" R8 insulated duct from my main exhaust duct to each hood independently.
Most people do not understand fans and duct. The rating it is given is without duct hooked to it. Just because its a 6" fan doesn't mean you HAVE to hook 6" duct to it.
If you hook 6" to it the fan will only move about 200 CFM. Inadequate.
If you give me details about your room ( size, layout, length of duct to exhaust) I can design you a sweet HVAC system. But be ready to drop some coin. I spent $300 on just my flex duct, and I get it as cheap as anyone can.